Factor. 3d^2 + 13d + 4 ____

Identify Variables: Identify a, b, and c in the quadratic expression 3d^2 + 13d + 4 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 13 c = 4Find Two Numbers: Find two numbers that multiply to a*c (which is 3*4=12) and add up to b (which is 13). The two numbers that satisfy these conditions are 1 and 12, since 1*12 = 12 and 1+12 = 13.Rewrite Middle Term: Rewrite the middle term, 13d, using the two numbers found in the previous step. 3d^2 + 13d + 4 can be rewritten as 3d^2 + 1d + 12d + 4.Group Terms: Group the terms into two pairs to factor by grouping. (3d^2 + 1d) + (12d + 4)Factor Out Common Factors: Factor out the greatest common factor from each pair. For the first pair, the greatest common factor is d, so we get d(3d + 1). For the second pair, the greatest common factor is 4, so we get 4(3d + 1).Final Factored Form: Since both groups contain the common factor (3d + 1), factor this out. The factored form is (d + 4)(3d + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3d^2 + 13d + 4

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $3d^2 + 13d + 4$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 13$ $\newline$ $c = 4$
Find Two Numbers: Find two numbers that multiply to $a*c$ (which is $3*4=12$ ) and add up to $b$ (which is $13$ ). $\newline$ The two numbers that satisfy these conditions are $1$ and $12$ , since $1*12 = 12$ and $1+12 = 13$ .
Rewrite Middle Term: Rewrite the middle term, $13d$ , using the two numbers found in the previous step. $\newline$ $3d^2 + 13d + 4$ can be rewritten as $3d^2 + 1d + 12d + 4$ .
Group Terms: Group the terms into two pairs to factor by grouping. $\newline$ $(3d^2 + 1d) + (12d + 4)$
Factor Out Common Factors: Factor out the greatest common factor from each pair. $\newline$ For the first pair, the greatest common factor is $d$ , so we get $d(3d + 1)$ . $\newline$ For the second pair, the greatest common factor is $4$ , so we get $4(3d + 1)$ .
Final Factored Form: Since both groups contain the common factor $(3d + 1)$ , factor this out. $\newline$ The factored form is $(d + 4)(3d + 1)$ .